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Mat. Zametki, 2010, Volume 87, Issue 5, Pages 756–763 (Mi mz8718)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem

A. G. Kachurovskiia, V. V. Sedalishchevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

Abstract: We study the rate of convergence in von Neumann's ergodic theorem. We obtain constants connecting the power rate of convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.

Keywords: von Neumann's ergodic theorem, ergodic mean, spectral measure, dynamical system, wide-sense stationary stochastic process, correlation coefficient, Darboux sum

DOI: https://doi.org/10.4213/mzm8718

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English version:
Mathematical Notes, 2010, 87:5, 720–727

Bibliographic databases:

UDC: 517.987+519.214
Received: 19.08.2009

Citation: A. G. Kachurovskii, V. V. Sedalishchev, “On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem”, Mat. Zametki, 87:5 (2010), 756–763; Math. Notes, 87:5 (2010), 720–727

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Kachurovskii, V. V. Sedalishchev, “Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems”, Sb. Math., 202:8 (2011), 1105–1125  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. N. A. Dzhulaǐ, A. G. Kachurovskiǐ, “Constants in the estimates of the rate of convergence in von Neumann's ergodic theorem with continuous time”, Siberian Math. J., 52:5 (2011), 824–835  mathnet  crossref  mathscinet  isi
    3. Kachurovskii A.G., Sedalischev V.V., “Neravenstva, pozvolyayuschie otsenivat skorosti skhodimosti v ergodicheskikh teoremakh”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 250–254  elib
    4. A. G. Kachurovskii, I. V. Podvigin, “Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems”, Trans. Moscow Math. Soc., 77 (2016), 1–53  mathnet  crossref  elib
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